We consider a shallow water equation of Camassa-Holm type, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solution of the dispersive equation converges to the unique entropy solution of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting.

A note on the convergence of the solutions of the Camassa-Holm equation to the entropy ones of a scalar conservation law / Coclite, Giuseppe Maria; di Ruvo, L.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 36:6(2016), pp. 2981-2990. [10.3934/dcds.2016.36.2981]

A note on the convergence of the solutions of the Camassa-Holm equation to the entropy ones of a scalar conservation law.

COCLITE, Giuseppe Maria;
2016-01-01

Abstract

We consider a shallow water equation of Camassa-Holm type, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solution of the dispersive equation converges to the unique entropy solution of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting.
2016
A note on the convergence of the solutions of the Camassa-Holm equation to the entropy ones of a scalar conservation law / Coclite, Giuseppe Maria; di Ruvo, L.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 36:6(2016), pp. 2981-2990. [10.3934/dcds.2016.36.2981]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/93820
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